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Logic circuits, truth tables and logic expressions Cambridge IGCSE Computer Science (9–1) revision

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In plain words

Join gates together and you have a logic circuit. The same circuit can be described in three ways: as a drawing, as a truth table, and as a logic expression such as X = (A AND B) OR (NOT C). The skill is moving between the three.

5 things to know

  1. A circuit with three inputs has eight rows in its truth table. Write them in binary counting order: 000, 001, 010, 011, 100, 101, 110, 111.
  2. To complete a truth table, add a column for the output of each gate inside the circuit. Work out those columns first, then the final output.
  3. To write an expression from a circuit, start at the inputs and write down what each gate does, using brackets to keep each gate's inputs together.
  4. To draw a circuit from an expression, draw one gate for each operator, working from inside the brackets outwards.
  5. From a problem statement: "and" becomes an AND gate, "or" becomes an OR gate, and "not" becomes a NOT gate. Draw the circuit as the statement is given, without simplifying it.

Worked example

Complete the truth table for X = (A AND B) OR (NOT C).

  1. Work out A AND B for the eight rows: 0, 0, 0, 0, 0, 0, 1, 1.
  2. Work out NOT C for the eight rows: 1, 0, 1, 0, 1, 0, 1, 0.
  3. OR the two columns together, row by row.
  4. X = 1, 0, 1, 0, 1, 0, 1, 1.

Worked example

An alarm (X) sounds if the system is switched on (S) and either a door is open (D) or a window is open (W). Write the logic expression.

  1. "Either a door or a window" is D OR W.
  2. That must happen together with the system being on: S AND (D OR W).
  3. X = S AND (D OR W).

Tips and tricks

  • Use the working columns. Trying to do a three-gate circuit in your head, eight times, is how rows go wrong.
  • Brackets matter. (A AND B) OR C is a different circuit from A AND (B OR C).
6 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Logic circuits, truth tables and logic expressions: 6 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. How many rows does a truth table for a circuit with three inputs have?
    • 3
    • 6
    • 8 (the answer)
    • 9

    2 × 2 × 2 combinations of inputs.

  2. A light (X) comes on if it is dark (D) and movement is detected (M). Which expression is correct?
    • X = D OR M
    • X = D AND M (the answer)
    • X = NOT D
    • X = D XOR M

    Both conditions are needed.

  3. What is the value of (A OR B) AND (NOT C) when A = 1, B = 0 and C = 1?
    • 0 (the answer)
    • 1
    • 2
    • it cannot be worked out

    A OR B is 1, but NOT C is 0, and 1 AND 0 is 0.

  4. What is the value of (A AND B) OR C when A = 1, B = 1 and C = 0?
    • 0
    • 1 (the answer)
    • 2
    • it cannot be worked out

    A AND B is 1, and 1 OR 0 is 1.

  5. Which single gate does the expression X = NOT (A AND B) describe?
    • NOR
    • NAND (the answer)
    • XOR
    • OR

    NAND is AND followed by NOT.

  6. Which expression matches this statement: X is 1 if A is 1, or if B is 1 and C is not 1?Stretch
    • X = (A OR B) AND (NOT C)
    • X = A OR (B AND (NOT C)) (the answer)
    • X = A AND (B OR (NOT C))
    • X = NOT (A OR B) AND C

    The "or" joins A to the whole of "B and not C".

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